yes it is, but I still don't understand the inclusion. Each of is a set (closed interval) containing infinitely many rational numbers bounded by the end points of each interval. Will their union include all rationals?

October 9th 2013, 10:45 AM

emakarov

Re: rationals and union of intervals that covers it

Quote:

Originally Posted by rayman

Will their union include all rationals?

Yes, it will. In my example, A ∪ B covers (i.e., is a superset of) the whole set {x, y} because each element of that set is covered by (i.e., belongs to) at least one of the sets in the union: either A or B. A completely parallel statement holds about ℚ and .

October 9th 2013, 10:51 AM

rayman

Re: rationals and union of intervals that covers it

Ah yes of course, I got it:) thank you

October 9th 2013, 10:55 AM

Plato

Re: rationals and union of intervals that covers it

Quote:

Originally Posted by rayman

I have a question, if is a sequence of all rational numbers, let
why do we have the following inclusion ?

Quote:

Originally Posted by rayman

yes it is, but I still don't understand the inclusion. Each of is a set (closed interval) containing infinitely many rational numbers bounded by the end points of each interval. Will their union include all rationals?